{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.05  m= 0  q0= 0.001  q1= 0.002\n",
      "0.1  m= 0  q0= 0.001  q1= 0.002\n",
      "0.15  m= 0  q0= 0.001  q1= 0.002\n",
      "0.2  m= 0  q0= 0.001  q1= 0.002\n",
      "0.25  m= 0  q0= 0.001  q1= 0.002\n",
      "0.3  m= 0  q0= 0.001  q1= 0.002\n",
      "0.35  m= 0  q0= 0.001  q1= 0.002\n",
      "0.4  m= 0  q0= 0.001  q1= 0.002\n",
      "0.45  m= 0  q0= 0.001  q1= 0.002\n",
      "0.5  m= 0  q0= 0.001  q1= 0.002\n",
      "0.55  m= 0  q0= 0.001  q1= 0.002\n",
      "0.6  m= 0  q0= 0.001  q1= 0.002\n",
      "0.65  m= 0  q0= 0.001  q1= 0.002\n",
      "0.7  m= 0  q0= 0.001  q1= 0.002\n",
      "0.75  m= 0  q0= 0.001  q1= 0.002\n",
      "0.8  m= 0  q0= 0.001  q1= 0.002\n",
      "0.85  m= 0  q0= 0.001  q1= 0.002\n",
      "0.9  m= 0  q0= 0.001  q1= 0.002\n",
      "0.95  m= 0  q0= 0.001  q1= 0.002\n",
      "1.0  m= 0  q0= 0.001  q1= 0.002\n",
      "1.05  m= 0.01  q0= 0.001  q1= 0.048243255790163024\n",
      "1.1  m= 0.07329062252203512  q0= 0.02986047145781406  q1= 0.09587333932328602\n",
      "1.15  m= 0.09895633813540453  q0= 0.046307569856816846  q1= 0.14008371685296728\n",
      "1.2  m= 0.11847939742355272  q0= 0.06079707233154409  q1= 0.18156805015472344\n",
      "1.25  m= 0.1339012043796615  q0= 0.07441998333779612  q1= 0.22037225176089772\n",
      "1.3  m= 0.1457269705631988  q0= 0.08689317964220147  q1= 0.2565405464422755\n",
      "1.35  m= 0.15508103876057033  q0= 0.09872634181216572  q1= 0.2902319828501685\n",
      "1.4  m= 0.1624675866355578  q0= 0.1098339874398794  q1= 0.32160332289867005\n",
      "1.45  m= 0.1682227110986354  q0= 0.12027681005758367  q1= 0.3508079784650492\n",
      "1.5  m= 0.17269845864297595  q0= 0.13011533959451596  q1= 0.37801149516830423\n",
      "1.55  m= 0.17613240647145492  q0= 0.1394197686748276  q1= 0.40336937688749486\n",
      "1.6  m= 0.1786972246919062  q0= 0.14819564143345293  q1= 0.42702528441024795\n",
      "1.65  m= 0.18055418733603332  q0= 0.15650282349539982  q1= 0.44911835617064866\n",
      "1.7  m= 0.18181489618055677  q0= 0.1643616329600785  q1= 0.4697724962993536\n",
      "1.75  m= 0.18258535656338962  q0= 0.17180536032024776  q1= 0.4891067429205108\n",
      "1.8  m= 0.18296072829422777  q0= 0.17889401039070696  q1= 0.5072290667086563\n",
      "1.85  m= 0.1829867044328143  q0= 0.18561518614933173  q1= 0.5242347066710856\n",
      "1.9  m= 0.18272259626950293  q0= 0.1920040271633078  q1= 0.5402122589291711\n",
      "1.95  m= 0.1822344720505709  q0= 0.1981046892746234  q1= 0.5552479564977513\n",
      "2.0  m= 0.18153863679697818  q0= 0.2039151188904315  q1= 0.5694094348991143\n",
      "2.05  m= 0.18067277493616038  q0= 0.20945277026210643  q1= 0.5827662210942032\n",
      "2.1  m= 0.17967288673658405  q0= 0.2147507972387522  q1= 0.5953805644604041\n",
      "2.15  m= 0.1785539811058933  q0= 0.21981276030035368  q1= 0.6073065453970077\n",
      "2.2  m= 0.17734412223164633  q0= 0.22466352744079687  q1= 0.6185968076747643\n",
      "2.25  m= 0.1760530157150812  q0= 0.22930693923826037  q1= 0.6292958970041075\n",
      "2.3  m= 0.17469863019373558  q0= 0.23376179224186394  q1= 0.6394467546612579\n",
      "2.35  m= 0.1732904862593544  q0= 0.23803361429900308  q1= 0.6490874255129744\n",
      "2.4  m= 0.17184111352267156  q0= 0.24213803286449945  q1= 0.6582537374389256\n",
      "2.45  m= 0.17036074299643944  q0= 0.24608406145990028  q1= 0.6669779255589472\n",
      "2.5  m= 0.16885354208789324  q0= 0.24987506923978006  q1= 0.6752895699075522\n",
      "2.55  m= 0.1673290171133429  q0= 0.2535282226883135  q1= 0.683215005103946\n",
      "2.6  m= 0.16579480089231197  q0= 0.25705036966638695  q1= 0.690781035501103\n",
      "2.65  m= 0.16424770840758984  q0= 0.26043349974414015  q1= 0.6980083863374598\n",
      "2.7  m= 0.1626990010198465  q0= 0.26370216540863917  q1= 0.7049192170858679\n",
      "2.75  m= 0.1611512078567667  q0= 0.266856816715728  q1= 0.7115335163116441\n",
      "2.8  m= 0.15960559522037923  q0= 0.269899752679886  q1= 0.7178682551392996\n",
      "2.85  m= 0.15806635819795092  q0= 0.27284175999875815  q1= 0.7239407686673336\n",
      "2.9  m= 0.15653455868806065  q0= 0.27568369849114777  q1= 0.7297660718392657\n",
      "2.95  m= 0.1550132884721622  q0= 0.278432128467903  q1= 0.7353587096841517\n",
      "3.0  m= 0.15350549065337082  q0= 0.28110076033825515  q1= 0.7407319169040025\n",
      "3.05  m= 0.15200772999156456  q0= 0.28367062756514794  q1= 0.7458974089183632\n",
      "3.1  m= 0.15052488805681885  q0= 0.2861624259777611  q1= 0.7508669041287642\n",
      "3.15  m= 0.14905788255004676  q0= 0.2885793848483625  q1= 0.7556512518887398\n",
      "3.2  m= 0.14760601111573024  q0= 0.29091919124333054  q1= 0.760260040249304\n",
      "3.25  m= 0.14617246166872677  q0= 0.2931944265623838  q1= 0.7647027706433752\n",
      "3.3  m= 0.1447554141045991  q0= 0.2953992871255005  q1= 0.7689877682753139\n",
      "3.35  m= 0.14335590651293098  q0= 0.2975400841004438  q1= 0.7731230598004488\n",
      "3.4  m= 0.14197407444401167  q0= 0.2996168328815442  q1= 0.7771163448075764\n",
      "3.45  m= 0.14061192479834023  q0= 0.3016395674763786  q1= 0.7809746785123683\n",
      "3.5  m= 0.13926563654036467  q0= 0.30359904700854423  q1= 0.7847040623999477\n",
      "3.55  m= 0.13793582501534132  q0= 0.30549525140429185  q1= 0.788309977259154\n",
      "3.6  m= 0.13663207978326752  q0= 0.30736446201310386  q1= 0.7918022965733398\n",
      "3.65  m= 0.13534157010303668  q0= 0.3091661011543706  q1= 0.795181329273958\n",
      "3.7  m= 0.13407001726510787  q0= 0.31092058508715936  q1= 0.7984546787210669\n",
      "3.75  m= 0.13281717857569034  q0= 0.31263036636093006  q1= 0.8016269666291247\n",
      "3.8  m= 0.1315833861059076  q0= 0.31429705443532824  q1= 0.8047026460167792\n",
      "3.85  m= 0.13036657189686776  q0= 0.31591723019546253  q1= 0.8076857767269479\n",
      "3.9  m= 0.12916832339738926  q0= 0.3174972496311315  q1= 0.8105806794788275\n",
      "3.95  m= 0.12798893189752852  q0= 0.3190407957312246  q1= 0.81339115924539\n",
      "4.0  m= 0.12682592445635185  q0= 0.32054335168369147  q1= 0.8161203614578945\n",
      "4.05  m= 0.12568054164556008  q0= 0.32200797447962043  q1= 0.8187721185295092\n",
      "4.1  m= 0.1245531445293342  q0= 0.32344045163531054  q1= 0.8213496123191617\n",
      "4.15  m= 0.12344225385206023  q0= 0.32483629917060447  q1= 0.8238556460819162\n",
      "4.2  m= 0.12234797179274354  q0= 0.32619847602989216  q1= 0.826293221017092\n",
      "4.25  m= 0.12126990446523163  q0= 0.3275271982561534  q1= 0.8286650087024929\n",
      "4.3  m= 0.12020902101980681  q0= 0.3288290144262487  q1= 0.8309738000938652\n",
      "4.35  m= 0.11916386913912318  q0= 0.3300992933049847  q1= 0.8332218589955263\n",
      "4.4  m= 0.11813413236178422  q0= 0.33133975940551064  q1= 0.8354114799759077\n",
      "4.45  m= 0.1171200035591722  q0= 0.33255274965096493  q1= 0.8375449609695258\n",
      "4.5  m= 0.11612120255826408  q0= 0.33373880954972335  q1= 0.8396244203157076\n",
      "4.55  m= 0.11513750059486591  q0= 0.3348991502081151  q1= 0.8416518770032448\n",
      "4.6  m= 0.1141684253650194  q0= 0.33603366772971777  q1= 0.8436291847775557\n",
      "4.65  m= 0.11321342902737068  q0= 0.3371422351129045  q1= 0.8455580875024402\n",
      "4.7  m= 0.11227343950896852  q0= 0.3382299538688872  q1= 0.8474405604487035\n",
      "4.75  m= 0.11134656853869622  q0= 0.33929127773773365  q1= 0.8492779408958995\n",
      "4.8  m= 0.1104342401054343  q0= 0.34033380408958785  q1= 0.8510721160755477\n",
      "4.85  m= 0.109534819801722  q0= 0.341352622650136  q1= 0.8528242953926541\n",
      "4.9  m= 0.10864940644605836  q0= 0.34235352542678105  q1= 0.8545362221450008\n",
      "4.95  m= 0.10777598249103632  q0= 0.34332967244678053  q1= 0.8562088789374809\n",
      "5.0  m= 0.1069156085218311  q0= 0.34428781987273127  q1= 0.8578438165687029\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import quad \n",
    "from scipy.special import jv\n",
    "from scipy.special import i0\n",
    "from scipy import integrate\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import optimize\n",
    "from scipy.optimize import LinearConstraint\n",
    "import math\n",
    "from scipy import special\n",
    "import scipy.stats\n",
    "from scipy import integrate\n",
    "\n",
    "def makeDiffPart(betaJ,m,q0,q1):\n",
    "    numHs=1001\n",
    "    hs,dh=np.linspace(0,10,numHs,retstep=True)\n",
    "    hs=hs+dh/2*(1-1/np.sqrt(3))\n",
    "    h0s,dh0=np.linspace(0,10,numHs,retstep=True)\n",
    "    h0s=h0s+dh0/2*(1-1/np.sqrt(3))\n",
    "    g1s=np.exp(betaJ**2*(1-q1))*i0(betaJ*np.sqrt(2)*hs)\n",
    "    mat=(hs/(q1-q0)*np.exp(-np.power(hs,2)/(2*(q1-q0))))[:,np.newaxis]*i0((hs[:,np.newaxis]*hs[np.newaxis,:])/(q1-q0))*np.power(g1s[:,np.newaxis],m)\n",
    "    g0s=np.sum(mat,axis=0)*dh0*np.exp(-np.power(h0s,2)/(2*(q1-q0)))\n",
    "    return np.sum(np.log(g0s)*h0s/q0*np.exp(-np.power(h0s,2)/(2*q0)))*dh0/m\n",
    "def makeDiffPartOther(betaJ,m,q0,q1):\n",
    "    def g1(h):\n",
    "        return np.exp(betaJ**2*(1-q1))*i0(betaJ*np.sqrt(2)*h)\n",
    "    def toIntegrate1(h,hx,hy):\n",
    "        sig2=(q1-q0)\n",
    "        return 1/(2*math.pi*sig2)*np.exp(-((h-hx)**2+hy**2)/(2*sig2))*g1(hx)**m\n",
    "    def g0(h):\n",
    "        sig=np.sqrt(q1-q0)\n",
    "        return integrate.dblquad(lambda hx,hy: toIntegrate1(h,hx,hy),h-40*sig,h+40*sig,-40*sig,40*sig)[0]\n",
    "    return integrate.quad(lambda h: np.log(g0(h))*h/q0*np.exp(-h**2/(2*q0)),0,10)[0]/m\n",
    "def makeDiffPartGood(betaJ,m,q0,q1):\n",
    "    numHs=2001\n",
    "    hs,dh=np.linspace(0,20,numHs,retstep=True)\n",
    "    hs=hs+dh/2*(1-1/np.sqrt(3))\n",
    "    g1s=np.exp(betaJ**2*(1-q1))*i0(betaJ*np.sqrt(2)*hs)\n",
    "    mat=(hs/(q1-q0))[:,np.newaxis]*special.i0e((hs[:,np.newaxis]*hs[np.newaxis,:])/(q1-q0))*np.power(g1s[:,np.newaxis],m)*np.exp(-np.square(hs[np.newaxis,:]-hs[:,np.newaxis])/(2*(q1-q0)))\n",
    "    g0s=np.sum(mat,axis=0)*dh\n",
    "    return 1/m*np.sum(np.log(g0s)*hs/q0*np.exp(-np.power(hs,2)/(2*q0)))*dh\n",
    "def logZDiff(betaJ,m,q0,qdiff):\n",
    "    q1=q0+qdiff\n",
    "    return -betaJ**2/2*(1+(m-1)*q1**2-m*q0**2)+makeDiffPartGood(betaJ,m,q0,q1)\n",
    "def logZBlock(betaJ, m,q):\n",
    "    if m==0:\n",
    "        return logZm0(betaJ,q)\n",
    "    def integrand(betaJ, x,y, q, m):\n",
    "        r=np.sqrt(np.square(x)[:,np.newaxis]+np.square(y)[np.newaxis,:])\n",
    "        return (1 / (4* math.pi * q * betaJ**2)) * (np.exp(-1 /(4*q * betaJ**2) * np.square(x))[:,np.newaxis]*np.exp(-1 / (4*q * betaJ**2) * np.square(y))[np.newaxis,:]) * np.power(special.i0(r),m)\n",
    "    first_term = -(betaJ**2 / 2)\n",
    "    second_term = -(m - 1) * (betaJ**2 / 2) * q**2\n",
    "    fourth_term = (betaJ**2) * (1 - q)\n",
    "\n",
    "    num=200\n",
    "    spread=30\n",
    "    xs,ys=np.linspace(-spread*betaJ*np.sqrt(q),spread*betaJ*np.sqrt(q),num+1),np.linspace(-spread*betaJ*np.sqrt(q),spread*betaJ*np.sqrt(q),num+1)\n",
    "    dx=2*spread*betaJ*np.sqrt(q)/num\n",
    "    tosum=integrand(betaJ, xs,ys, q, m)\n",
    "    fifth_term = np.log(integrate.simps(integrate.simps(tosum,axis=1),axis=0)*dx**2)/m\n",
    "    result = first_term + second_term + fourth_term+fifth_term\n",
    "    #print(toSum[-1])\n",
    "    return result.real\n",
    "def logZm0(betaJ,q):\n",
    "    def integrandm0(betaJ,r, q):\n",
    "        return np.log(jv(0,1j*r)).real*(r / (2*q * betaJ**2)) * np.exp(-1 / (4*q * betaJ**2) * r**2)\n",
    "    first_term = -(betaJ**2 / 2)\n",
    "    second_term = (betaJ**2 / 2) * q**2\n",
    "\n",
    "    integrand_func = lambda r: integrandm0(betaJ,r, q)\n",
    "    integral = quad(integrand_func, 0, 8*(12+5*m*betaJ**2))[0]\n",
    "\n",
    "    third_term = (betaJ**2 ) * (1 - q)\n",
    "    fourth_term = integral\n",
    "\n",
    "    result = first_term + second_term + third_term + fourth_term\n",
    "    return result.real\n",
    "#print(makeDiffPartOther(2,0.1,.7,.9))\n",
    "#minimize subject to 0<q0<q1<1, 0<m<1\n",
    "numBetaJs=100\n",
    "betaJs=np.linspace(5/numBetaJs,5,numBetaJs)\n",
    "q0s=np.zeros(numBetaJs)\n",
    "q1s=np.zeros(numBetaJs)\n",
    "ms=np.zeros(numBetaJs)\n",
    "logZsRSB=np.zeros(numBetaJs)\n",
    "for i in range(numBetaJs):\n",
    "    betaJ=betaJs[i]\n",
    "    #use different methods for same optimization\n",
    "    mGuess=min(max(0,(betaJ-1))+.00002,1)\n",
    "    qGuess=min(np.sqrt(max(0,(betaJ**2-1)))+.00002,1)\n",
    "    res=optimize.minimize(lambda x: logZBlock(betaJ,x[0],x[1]),x0=[mGuess,qGuess],bounds=[(.00001,1.0),(0.0001,1)],tol=1e-12,method='L-BFGS-B')\n",
    "    q=res.x[1]\n",
    "    m=res.x[0]\n",
    "    optimAnswer=scipy.optimize.minimize(lambda x: logZDiff(betaJs[i],x[0],x[1],x[2]),x0=[m,q/2,q/2],bounds=[(0.01,0.2),(0.001,1),(0.001,1)],method='L-BFGS-B',tol=1e-12)\n",
    "    x=optimAnswer.x\n",
    "    logZsRSB[i]=optimAnswer.fun\n",
    "    q1=x[2]+x[1]   \n",
    "    q0=x[1]\n",
    "    m=x[0]\n",
    "    ms[i]=m\n",
    "    q0s[i]=q0\n",
    "    q1s[i]=q1\n",
    "    if q1-q0<.002:\n",
    "        m=0\n",
    "        ms[i]=m\n",
    "    print(round(betaJs[i],2),\" m=\",m,\" q0=\",q0,\" q1=\",q1)\n",
    "plt.plot(betaJs,q0s,label=\"q0\")\n",
    "plt.plot(betaJs,q1s,label=\"q1\")\n",
    "plt.title(r'$q_1$ and $q_0$')\n",
    "plt.xlabel(r'$\\beta J$')\n",
    "plt.ylabel(r'$q$')\n",
    "plt.legend()\n",
    "plt.savefig('q1q0.pdf',dpi='figure')\n",
    "plt.show()\n",
    "plt.plot(betaJs,ms)\n",
    "plt.title(r\"$m$\")\n",
    "plt.xlabel(r'$\\beta J$')\n",
    "plt.ylabel(r'$m$')\n",
    "plt.savefig('m.pdf',dpi='figure')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.special import i0,i1,iv\n",
    "from scipy.special import i0e,i1e,ive\n",
    "from scipy import integrate\n",
    "from scipy import optimize\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def qCorrs(betaJ,q):\n",
    "    def integrandabcd(r):\n",
    "        return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(i1e(r)/i0e(r))**4\n",
    "    def integrandabc(r):\n",
    "        return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(ive(2,r)*i1e(r)**2/i0e(r)**3+i1e(r)**2/i0e(r)**2)/2\n",
    "    def integrandab(r):\n",
    "        return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(1+ive(2,r)**2/i0e(r)**2)/2\n",
    "    upLim=200\n",
    "    corrabcd=integrate.quad(integrandabcd,0,upLim)[0]-q**2 #(n choose 4)*3*2\n",
    "    corrabc=integrate.quad(integrandabc,0,upLim)[0]-q**2 #n*(n-1)*(n-2)\n",
    "    corrab=integrate.quad(integrandab,0,upLim)[0]-q**2 #n choose 2\n",
    "    return corrabcd,corrabc,corrab\n",
    "def Ztheta(betaJ,q):\n",
    "    def integrandZ(r):\n",
    "        return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(np.log(i0e(r))+r)\n",
    "    upLim=20*betaJ*(np.sqrt(q))\n",
    "    Z=integrate.quad(integrandZ,0,np.inf)[0]+betaJ**2*(1-q)\n",
    "    return Z\n",
    "def Ztheta(betaJ,q):\n",
    "    def integrandZ(r):\n",
    "        return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(np.log(i0e(r))+r)\n",
    "    rs,dr=np.linspace(0,150*betaJ*(np.sqrt(q)),2000,retstep=True)\n",
    "    integrandZs=integrandZ(rs)\n",
    "    Z=np.sum(integrandZs)*dr+betaJ**2*(1-q)\n",
    "    return Z\n",
    "def logZRS(betaJ,q):\n",
    "    logZ=-betaJ**2/2+betaJ**2*q**2/2+Ztheta(betaJ,q)\n",
    "    return logZ\n",
    "numBetaJs=100\n",
    "betaJs=np.linspace(5/numBetaJs,5,numBetaJs)\n",
    "qs=np.zeros(len(betaJs))\n",
    "logZsRS=np.zeros(len(betaJs))\n",
    "for i in range(len(betaJs)):\n",
    "    betaJ=betaJs[i]\n",
    "    res=optimize.minimize_scalar(lambda q: logZRS(betaJ,q),bounds=(0,1),method='bounded')\n",
    "    q=res.x\n",
    "    qs[i]=q\n",
    "    logZsRS[i]=logZRS(betaJ,q)\n",
    "plt.plot(betaJs,qs)\n",
    "plt.xlabel(r'$\\beta J$')\n",
    "plt.ylabel(r'$q$')\n",
    "plt.title(r'Replica Order at $\\beta J=1$')\n",
    "plt.savefig('qRS.pdf',bbox_inches='tight',dpi=300)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(betaJs,logZsRSB)\n",
    "plt.title(r\"$\\log Z$\")\n",
    "plt.xlabel(r'$\\beta J$')\n",
    "plt.ylabel(r'$\\log Z$')\n",
    "plt.savefig('logZ.pdf',dpi='figure')\n",
    "plt.show()\n",
    "plt.plot(betaJs,logZsRSB-logZsRS,label=\"RSB\")\n",
    "plt.title(r\"$\\log Z$\")\n",
    "plt.xlabel(r'$\\beta J$')\n",
    "plt.ylabel(r'$\\log Z$')\n",
    "plt.legend()\n",
    "plt.savefig('logZCompare.pdf',dpi='figure')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
